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Thread: Circle question

  1. #1
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    Circle question

    If you draw a circle inside a square and the circle fits exactly inside the square, how many percents of the square does the circle cover?

    I need an easy and understandable formula and the result too if possible. Thanks!
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  2. #2
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    Quote Originally Posted by Shandy View Post
    If you draw a circle inside a square and the circle fits exactly inside the square, how many percents of the square does the circle cover?

    I need an easy and understandable formula and the result too if possible. Thanks!
    A circle inside a square of sidelength $\displaystyle x$ has a radius of $\displaystyle \frac{x}{2}$.

    Substitute this data into the usual formulae for the area of a square and the area of a circle. Then calculate the percentage of area covered.
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  3. #3
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    Correct or not?

    Is my result correct or not?

    A perfectly fit circle inside a square covers 80% of the square.
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  4. #4
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    Quote Originally Posted by Shandy View Post
    Is my result correct or not?

    A perfectly fit circle inside a square covers 80% of the square.
    If the radius of the circle is $\displaystyle r$, then the sides of the square are of length $\displaystyle 2r$.

    So the fraction of the square that is covered is $\displaystyle \frac{\pi r^2}{(2r)^2} = \frac{\pi}{4}$, which is about 0.78, so you are about right.

    Grandad

    Last edited by mr fantastic; Feb 5th 2009 at 03:09 AM. Reason: No edit - just flagging the reply as having been moved from another thread.
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